Topics in Spatial Epidemiology
Tutorials on spatial epidemiology topics built by Jon Zelner.
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In this tutorial, we’re going to walk through ways in which patterns of residential segregation may impact infectious disease risk through two different pathways, contact and susceptibility, and how that is likely to impact spatial and socioeconomic patterns of infection incidence.
To do this, we’ll build on the framework developed by Acevedo-Garcia (2000) to relate the social processes governing and generating residential segregation to the biological manifestations of disease.
Specifically, we’ll first walk through the hypothesized relationships between segregation and patterns of contact. We’ll then take a hands-on approach to understanding the way different intensities and modalities of segregation impact patterns of within and between-group contact. Finally, we’ll put these contact patterns into an infectious disease transmission model and look at their implications for risk, both at the population and group level.
Acevedo-Garcia (2000) presented a helpful model of the relationship between residential segregation and infectious disease risk. Specifically, she identified a number of different measures of the intensity of segregation and hypothesized about their potential relationships to infection risk. She focused on Tuberculosis, but we can think of this as a more general approach.
In this model, the world is broken down into two groups, majority and minority. Typically, residential segregation can be thought of in racial or socioeconomic terms. But at the end of the day, all of the insights about segregation are applicable to thinking about patterns of contact and risk in any setting where you have two interacting populations, and differing rates of within and between-group contact.
It’s also important to remember that these processes occur in many contexts and not only along the lines we typically think of as characterizing residential segregation in the United States. For example, in many countries, recent arrivals to a city from the countryside may live in shantytowns that induce higher rates of within-group contact as well as a higher intensity of exposure due to local environmental and social factors.
After reviewing the literature and the different approaches to measuring segregation, she concludes that disparities in infection risk related to segregation can be conceptualized primarily as a function of two attributes, specifically:
For example, this image shows a situation of low isolation in which members of the minority group (in green) are evenly distributed throughout neighborhoods of a hypothetical city:
Specifically, the green individuals represent 10% of the population and are evenly dispersed throughout, so that each block has 10% of its members from the green group and 90% from the red group, reflecting the population distribution.
By contrast, this image shows a situation in which isolation is very high, where green individuals only contact other green individuals, and the same goes for those in the red group:
In the next section, we will explore how these factors come together to impact patterns and intensities of contact within and between minority and majority groups.
In this demo, you can explore the impact of some key parameters on the distribution of contacts an individual has. The plots show you 100 contacts of individuals in the minority (green) and majority (red) groups, respectively. The size of the dots indicates the relative susceptibility of individuals in the segregated minority group. We can think of the susceptibility as multiplying the risk of infection.
One thing to pay attention to is what happens when isolation < proportion in the minority group. In a well-mixed population, i.e. where individuals contact each other without regard to group membership, isolation = proportion in the minority group. When isolation is lower than the proportion in the group, this means that individuals in that group preferentially have contact with those in the majority group.
When we talk about the relationship between segregation and infectious disease disparities, we’re really talking about the way that segregation impacts rates of transmission within and between the two groups. In this sense, isolation is really only part of the equation: the other one is interaction, i.e. how much contact does the minority group have with the majority group and vice-versa. In a scenario with just two groups, this is simple: The interaction of minority group members with majority group members is just 1-isolation, i.e. the proportion of contacts not used up by within-group contact.
Now, let’s think about how these factors, of isolation, concentration, and susceptibility, may related to the dynamics of transmission.
The diagram below shows the states susceptible-infected-recovered model with two groups, representing the red majority group individuals and the green minority group individuals:
For a refresher on SIR Models check out the Wikipedia page, and this tutorial.
Briefly, in this model, individuals can be in one of the three states. Susceptible individuals (marked by S) are those who are able to be infected, infected individuals are those can infect susceptible individuals and move them into the I class. Finally, in this model, when an individual recovers after some period of time, they enter the R class and are assumed to be immune from future infection.
We’ll extend the basic SIR model by splitting everyone up into two groups, with one set of disease states for the red majority group members and another for the green minority group members. We’ve added two more parameters to the contact ones from the last exercise. Now we have the daily infectiousness, i.e. the risk that a majority group individual with infect another majority group individual on each day. We have also added the average duration of infection in days. The second parameter is the average duration of infectiousness. Remember, more days on which to be infectious = more infections if you keep the daily infectiousness constant.
The contact parameters are the same as before, but now they are governing the rate of contact both within and between the majority and minority groups.
The rate of transmission is a function of who you contact as well as how likely those contacts are to infect you. So, if susceptibility = 2, for each infectious individual they are exposed to, a susceptible individual in the minority group would have double the risk of infection as an equivalent individual in the majority group.
For example, this might occur in a situation where individuals in the minority group live in more cramped conditions with poor air circulation, making the likelihood of infection upon exposure greater for those in the minority than the majority. For vaccine-preventible diseases, it could be the case that individuals in the minority group are less likely to be vaccinated than those in the majority, making them more susceptible to infection.
The value \(R0\) at the bottom is the basic reproduction number, i.e. the average number of individuals infected by single case in a totally susceptible population. This value is important because if \(R0 > 1\), we should expect to see outbreaks, but if it is less than 1, we should expect transmission to fizzle out.
Try different values of the slider and press “Run Model!” to update the output. In the figure, the red line represents the total number of infections in the majority group, the green line represents the total number of infections in the minority group, and the black line is the total overall out of a population of 100,000 individuals. The red and green dashed lines show the maximum number of possible infections for the majority and minority groups, respectively.
The text below the plot shows the final proportion of the population of each group that was infected at the end of the simulation, as well as the relative risk of infection for individuals in the minority vs. majority group. Use this information as well as your observations from running the transmission model with different input parameter values to think about the following questions:
What seems to be the most important factor in driving inequality in the number of infections at the end of the outbreak?
Is there a relationship between infectiousness and inequality? In other words, is inequality in infection risk greater or lower at high levels of infectiousness?
What impact does the susceptibility of the minority group have on population-level patterns of disease? Are there situations in which the minority group may have very high rates of infection, but the population as a whole does not? When does this happen?